Series: Graduate Texts in Mathematics , Preliminary entry 632
2007, Approx. 320 p. 60 illus., Hardcover
ISBN: 0-387-33841-1
About this textbook
Braids and braid groups have been at the heart of important
mathematical developments over the last two decades. Introduced
to the field of mathematics by Artin in the 1920fs, their
association with permutations has led to their presence in a
number of mathematical fields and even physics. They form central
objects in knot theory and three-dimensional topology and have
led to the creation of a new field called quantum topology.
Important results related to their linearity and orderability
have fostered a lot of mathematical activity.
Braids and braid groups form the central topic of this text. The
authors begin with an introduction to the basic theory
highlighting the several definitions of braid groups and showing
their equivalence. The relationship between braids, knots and
links is then investigated. Recent developments in this field
follow next, with a focus on the linearity and orderability of
braid groups. This excellent presentation is motivated by
numerous examples and problems. Five elaborate appendices
containing additional relevant material complete the text.
Based on lectures given by the authors at the Bourbaki Seminar
and in a graduate course, this well-written book is ideal for
graduate students and all mathematicians that would like to be
introduced to the fascinating world of braids and braid groups.
Table of contents
Braids and Braid Groups.- Braids, Knots, and Links.- Burau
Representation.- Garside Monoids and Braid Monoids.-
Representations and the Iwahori-Hecke Algebras.- Orderings.-
Appendix A. Free Groups and Magnus Expansion.- Appendix B.
Fibrations and Homotopy Sequences.- Appendix C. The Symmetric
Groups.- Appendix D. Representations of Finite Groups and Finite-dimensional
Algebras.- Appendix E. Presentations of the Modular Group.- Notes.-
Bibliography.- Index
Series: Progress in Mathematical Physics , Preliminary entry
1520
2007, Approx. 295 p. 10 illus., Hardcover
ISBN: 0-8176-4502-0
About this textbook
This text examines functions on Rn (rather than spinor-valued
functions) with values in the Clifford algebra in higher
dimensions. There is a close connection between the higher
dimensional analogues of the Dolbeault complex and properties of
solutions of higher spin analogues of the Rarita?Schwinger
equations. An examination of a number of related questions that
are now well understood forms the main topic of this book.
Two different methods are presented in parallel for describing
function theory for higher spin equations. One is based on
results and language developed over many decades in the Clifford
analysis setting; the other on differential geometry, in
particular, from recent research concerning invariant
differential operators on manifolds with a given parabolic
structure.
Table of contents
Preface.- Prolog: Conformally Invariant Equations on the Sphere.-
Two Dirac Equations.- Symmetric Analogues of Rarita--Schwinger
Equations.- The Three-dimensional Case.- The Four-dimensional
Case.- Avenues for Future Research.- Appendix 1: Conformally
Invariant First-order Differential Equations on Manifolds.-
Appendix 2: Representation Theory of the Orthogonal Group.-
Blibliography.- Index.
Series: Progress in Mathematical Physics , Preliminary entry
1510
2007, Approx. 400 p. 49 illus., Hardcover
ISBN: 0-8176-4498-9
About this book
This book provides a comprehensive survey of the state-of-the-art
in the development of the relativity theory of scales. This
theory suggests an original solution to the disunified nature of
the classical-quantum transition in physical systems, enabling
quantum mechanics to be based on the principle of relativity
provided this principle is extended to scale transformations of
the reference system.
In the framework of such a newly-generalized relativity theory (including
position, orientation, motion and scale transformations), the
fundamental laws of physics may be given a general form that
transcends and integrates the classical and the quantum regimes.
A related concern of this book is the geometry of space-time,
particularly at small scales. Analogous to Einstein's
construction of general relativity (of motion) based on the
generalization of flat space-time to curved Riemannian space-time,
scale relativity suggests a generalization based on non-differentiable
and fractal geometry.
Part I addresses the current state of the theory, introduces new
mathematical and physical tools, reviews recent developments, and
considers open questions. Part II is devoted to applications to
high energy physics, astrophysics, and cosmology. Part III is
concerned with applications in biology and the life sciences:
species and societal evolution, embryogenesis and fundamental
biological processes.
By collecting and organizing developments and applications from
diverse fields, it is hoped that this monograph will serve as a
reference for graduate students and researchers interested in the
foundations of physics, quantum mechanics, astronomy, cosmology,
the life sciences, self-organization processes, and scale-dependent
phenomena. Prerequisites are limited to a basic knowledge of
classical and quantum mechanics, special and general relativity,
and fluid mechanics.
Table of contents
Preface.- Part I: Theory.- Introduction.- Structure of the Theory.-
From Non-differentiability to Fractality.- Scale Laws.- Fractal
Space and Induced Quantum Mechanics.- Fractal Space-time and
Relativistic Quantum Mechanics.- Gauge Theories and Scale
Relativity.- Quantum Mechanics in Scale-Space.- Part II:
Applications to Physics.- Application to Elementary Particle and
High Energy Physics.- Application to Gravitational Structuring.-
Application to Cosmology.- Part III: Applications to Social and
Life Sciences.- Application of Scale Laws to Sciences of Life.-
Application of Generalized Quantum Laws to Sciences of Life.-
Application of New Quantum Mechanics in Scale-Space.- Future
Prospects.- Conclusion.- References.- Index.
Series: Mathematical Concepts and Methods in Science and
Engineering , Vol. 51
Approx. 385 p., 2007, Approx. 380 p. 40 illus., Hardcover
ISBN: 0-387-31052-5
About this textbook
Linear vibrations is a topic of central interest in numerous
fields of engineering and is widely applicable to civil,
mechanical, aerospace, and biomedical engineering. This book
deals with the elements of the theory of linear vibrations and
its applications.
The theory of linear vibrations is systematically developed
starting from the basics. In a systematic manner, the author
deals with single-degree of freedom systems before progressing to
the more complex multi-degree of freedom systems. Topics such as
Laplace transforms, complex frequency responses, elements of
feedback control and aspects of time-delayed control and its
applications are discussed at the end. A set of graded problems,
to exercise the understanding of the student, is provided at the
end of each chapter. Numerous illustrative examples are provided
in each chapter alongside the development of the theory. In
addition, there are two chapters specifically devoted to
illustrative examples and applications.
By including topics from stability and control theory, the book
aims to provide the student with a broader view of the
application areas to which the theory is germane. It is meant to
be a text for a one semester, first course, on the subject,
suitable for seniors and/or first year graduate students in
engineering. Applied mathematicians will also find this book
useful.
Table of contents
Basic Mechanics, Single Degree of Freedom Systems.- Undamped
Single Degree of Freedom (SDOF) Systems, Free Vibrations.- Damped
SDOF Systems, Free Vibrations.- Harmonic Excitation of Damped
SDOF Systems, Resonance.- Isolation of Instruments and
Foundations, Motion Sensing Instrumentation.- Response of Damped
SDOF Systems to General Excitations.- Damping in Structural and
Mechanical Systems, Viscous, Structural, Bouc-Wen, and Coulomb
Damping.- Illustrative Examples and Applications of SDOF Systems.-
Laplace Transforms, Complex Frequency Response; Elements of
Structural Feeddback Control, Time-Delayed Control.- Two Degree
of Freedom Systems, Eigenvalues, Mode Shapes, Modal Frequencies.-
Classically and non-classically Damped Multi-degree of Freedom
Systems(MDOF).- generalized coordinates, Lagrange's Equations,
Linearization, and Equivalent linearization; Stability, Examples.-
Elements of Feedback Control of MDOF Systems.- Illustrative
Examples and Applications of MDOF Systems.- An Introduction to
Continuous Systems
2005, XXII, 231 p. with numerous figs., Hardcover
ISBN: 3-211-25210-X
About this book
Space and Time are the prison bars of reality. Space Time Physics
and Fractality is an attempt to tunnel through the rigidity of it
all ? by turning everything into dust or smoke. These two ancient
traditions are brought together here for the first time ? in the
spirit of Democritus and Anaxagoras. Mohamed El Naschie, the
sexagenarian, is the "dust dragon". The book contains
papers by people who are infected by the same virus of
desperately wanting to understand, and represents an incomparable
breakthrough. Not for the feebleminded, however.
Table of contents
Foreword.- Elnashai, A.: Recollections.- Martienssen, W.:
Congratulations.- Grigolini, P.: Quantum Mechanics and Non-Ordinary
Statistical Mechanics.- Ord, G. N.: Bohr, Bohm and Entwined Paths.-
Nottale, L.: On the Transition from the Classical to the Quantum
Regime in Fractal Space-Time Theory.- Rossler, O. E.: Needle
People and Pancake People: The Gulliver Effect.- Finkelstein, D.
R.: Cosmic Computation.- Greiner, W., Solovfyov, A.: Atomic
Cluster Physics: New Challenges for Theory and Experiment.-
Kroger, H.: Why are Probabilistic Laws Governing Quantum
Mechanics and Neurobiology?.- Sidharth, B. G.: Ramifications of
Non Commutative Spacetime.- Svozil, K.: Computational Universes.-
Diebner, H. H., Grond, F.: Usability of Synchronization for
Cognitive Modeling.- Kapitaniak, T.: Riddling Bifurcation and ...
Interstellar Journeys.- de Boer, R.: Theoretical Poroelasticity ?
A New Approach.- El Naschie, M. S.: From Hilbert space to the
number of Higgs particles via the quantum two-slit experiment